Check if a large number can be divided into two or more segments of equal sum

Given a very large Number N. The task is to check if the number can be divided into two or more segments of an equal sum.

Examples:

Input: N = 73452  
Output: Yes
Segments of {7}, {3, 4}, {5, 2} which has equal sum of 7

Input: N = 1248
Output: No

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The following steps can be followed to solve the problem:

Since the number can be large, the number is initialized in a string.
Use prefixSum array to store the prefix sum of the array.
Now traverse from second element to last, and the first segment thus will be 0 to i-1, whose sum is Prefixsum[i-1].
Use another pointer which traverses from i to n, and keep adding the sum.
If the sum at any stage is equal to Prefixsum[i-1], then the segment has a sum equal to first.
Reinitialize the segment sum value to 0 and keep moving the pointer.
If at any stage the segment sum exceeds the sum of the first segment, then break, as the division with segment sum as prefixsum[i-1] is not possible.
If the pointer reaches the last number, check if the last segment sum is equal to the first segment sum i.e., prefixsum[i-1], then it can be divided into segments of equal sum.

Below is the implementation of the above approach.

C++

// C++ program to Check if a large number can be divided  
// into two or more segments of equal sum 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to check if a number 
// can be divided into segments 
bool check(string s) 
{ 
    // length of string 
    int n = s.length(); 
  
    // array to store prefix sum 
    int Presum[n]; 
  
    // first index 
    Presum[0] = s[0] - '0'; 
  
    // calculate the prefix 
    for (int i = 1; i < n; i++) { 
        Presum[i] = Presum[i - 1] + (s[i] - '0'); 
    } 
  
    // iterate for all number from second number 
    for (int i = 1; i <= n - 1; i++) { 
  
        // sum from 0th index to i-1th index 
        int sum = Presum[i - 1]; 
        int presum = 0; 
        int it = i; 
  
        // counter turns true when sum 
        // is obtained from a segment 
        int flag = 0; 
  
        // iterate till the last number 
        while (it < n) { 
            // sum of segments 
            presum += s[it] - '0'; 
  
            // if segment sum is equal 
            // to first segment 
            if (presum == sum) { 
                presum = 0; 
                flag = 1; 
            } 
            // when greater than not possible 
            else if (presum > sum) { 
                break; 
            } 
            it++; 
        } 
  
        // if at the end all values are traversed 
        // and all segments have sum equal to first segment 
        // then it is possible 
        if (presum == 0 && it == n && flag == 1) { 
            return true; 
        } 
    } 
    return false; 
} 
  
// Driver Code 
int main() 
{ 
    string s = "73452"; 
    if (check(s)) 
        cout << "Yes"; 
    else
        cout << "No"; 
    return 0; 
} 

Java

// Java program to Check if a large number can be divided  
// into two or more segments of equal sum 
  
public class GFG { 
  
    // Function to check if a number 
    // can be divided into segments 
    static boolean check(String s) 
    { 
        // length of string 
        int n = s.length(); 
       
        // array to store prefix sum 
        int[] Presum = new int[n]; 
       
        // first index 
        char[] s1 = s.toCharArray(); 
        Presum[0] = s1[0] - '0'; 
       
        // calculate the prefix 
        for (int i = 1; i < n; i++) { 
            Presum[i] = Presum[i - 1] + (s1[i] - '0'); 
        } 
       
        // iterate for all number from second number 
        for (int i = 1; i <= n - 1; i++) { 
       
            // sum from 0th index to i-1th index 
            int sum = Presum[i - 1]; 
            int presum = 0; 
            int it = i; 
       
            // counter turns true when sum 
            // is obtained from a segment 
            int flag = 0; 
       
            // iterate till the last number 
            while (it < n) { 
                // sum of segments 
                presum += s1[it] - '0'; 
       
                // if segment sum is equal 
                // to first segment 
                if (presum == sum) { 
                    presum = 0; 
                    flag = 1; 
                } 
                // when greater than not possible 
                else if (presum > sum) { 
                    break; 
                } 
                it++; 
            } 
       
            // if at the end all values are traversed 
            // and all segments have sum equal to first segment 
            // then it is possible 
            if (presum == 0 && it == n && flag == 1) { 
                return true; 
            } 
        } 
        return false; 
    } 
       
    // Driver Code 
    public static void main(String[] args) { 
          
        String s = "73452"; 
        if (check(s)) 
            System.out.println("Yes"); 
        else
            System.out.println("No"); 
    } 
} 

Python 3

# Python program to Check if a large number can be divided  
# into two or more segments of equal sum 
# Function to check if a number  
# can be divided into segments  
def check(s) : 
  
    # length of string  
    n = len(s) 
  
    # array to store prefix sum  
    Presum = [0] * n 
  
    # ord() gives ASCII value 
    # first index  
    Presum[0] = ord(s[0]) - ord('0') 
  
    # calculate the prefix  
    for i in range(n) : 
        Presum[i] = Presum[i - 1] + (ord(s[i]) - ord('0')) 
  
    # iterate for all number from second number 
    for i in range(n) : 
  
        # sum from 0th index to i-1th index  
        sum = Presum[i] 
        presum = 0
        it = 1
  
        #  counter turns true when sum  
        # is obtained from a segment 
        flag = 0
  
        # iterate till the last number 
        while( it < n) : 
  
            # sum of segments                          
            presum += ord(s[it]) - ord('0')                              
  
            # if segment sum is equal  
            # to first segment  
            if presum == sum : 
                presum = 0
                flag = 1
  
            # when greater than not possible                         
            elif presum > sum :                 
                break
                                       
            it += 1
  
        # if at the end all values are traversed  
        # and all segments have sum equal to first segment  
        # then it is possible  
        if presum == 0 and it == n and flag == 1 : 
            return True
  
    return False
  
                                       
# Driver Code 
if __name__ == "__main__" : 
  
    s = "73452"
    if check(s) : 
        print("Yes") 
    else : 
        print("No") 
  
# This code is contributed by ANKITRAI1 

C#

// C# program to Check if a large 
// number can be divided into two 
// or more segments of equal sum  
using System; 
  
class GFG  
{  
  
    // Function to check if a number  
    // can be divided into segments  
    static bool check(String s)  
    {  
        // length of string  
        int n = s.Length;  
      
        // array to store prefix sum  
        int[] Presum = new int[n];  
      
        // first index  
        char[] s1 = s.ToCharArray();  
        Presum[0] = s1[0] - '0';  
      
        // calculate the prefix  
        for (int i = 1; i < n; i++)  
        {  
            Presum[i] = Presum[i - 1] + (s1[i] - '0');  
        }  
      
        // iterate for all number from second number  
        for (int i = 1; i <= n - 1; i++)  
        {  
      
            // sum from 0th index to i-1th index  
            int sum = Presum[i - 1];  
            int presum = 0;  
            int it = i;  
      
            // counter turns true when sum  
            // is obtained from a segment  
            int flag = 0;  
      
            // iterate till the last number  
            while (it < n)  
            {  
                // sum of segments  
                presum += s1[it] - '0';  
      
                // if segment sum is equal  
                // to first segment  
                if (presum == sum) 
                {  
                    presum = 0;  
                    flag = 1;  
                }  
                  
                // when greater than not possible  
                else if (presum > sum) 
                {  
                    break;  
                }  
                it++;  
            }  
      
            // if at the end all values are traversed  
            // and all segments have sum equal to first segment  
            // then it is possible  
            if (presum == 0 && it == n && flag == 1) 
            {  
                return true;  
            }  
        }  
        return false;  
    }  
      
    // Driver Code  
    public static void Main(String[] args)  
    {  
          
        String s = "73452";  
        if (check(s))  
            Console.WriteLine("Yes");  
        else
            Console.WriteLine("No");  
    }  
}  
  
// This code has been contributed by 29AjayKumar 

Output:

Yes

Time Complexity: O(N²)
Auxiliary Space: O(N)

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python 3

C#

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